The pulsed ultrasonic method has been applied to the determination of the stiffness coefficients for beryllium. The constants $c_{11}=30.8\mathrm{}\times {10}^{11}$ dynes/${\mathrm{cm}}^2$, $c_{33}=35.7\mathrm{}$ were evaluated from compressional wave velocities in single crystals by extrapolating a plot of the effective stiffness coefficient versus ${sin}^2\theta$ $\theta$ being the angle between the hexagonal axis and the direction of wave propagation) to the points $\theta =\frac{\pi }{2} \mathrm{and} 2\mathrm{and} 0$. The values $c_{12}=-5.8\mathrm{}$, $c_{44}=11.0\mathrm{}$ were derived from an analysis relating the average effective stiffness stiffness coefficients for compressional and shear waves with the shear modulus and Lame's constant. The latter data were calculated from measurements of longitudinal and transverse body wave velocities in polycrystalline metal. To find the coefficient $c_{13}=0.87\mathrm{}$, the established values for the other constants were employed in the general relation for the effective stiffness coefficient of the form $C_l=f(c_{j{k}^{\prime }}s,\theta )$. Several criteria have been used to assess the validity of the $c_{\mathrm{jk}}$ data: (1) The ratio of $\frac{c_{11}}{c_{33}}$ is in accord with the $\frac{c}{a}$ ratio for the hexagonal close-packed structure of beryllium; (2) the compressional and shear wave anisotropy factors of $\frac{c_{33}}{c_{11}}=1.16\mathrm{}$ and $\frac{c_{44}}{\frac{1}{2}(c_{11}-c_{12})}=1.68\mathrm{}$, respectively are in harmony with the observed transmission properties of polycrystalline beryllium; and (3) the experimental and theoretical curves for the directional variation of the effective compressional stiffness coefficient agree quite well.

Close

PrevNext

View figure in article